Toilet Paper

[didds]

Many thanks for that but I have to say that I did not understand a word of it. It looks convincing though, so I will accept it.

Dod

You are not alone Dod

[GoSeigen]

seems this explains (?!) it all...

https://en.wikipedia.org/wiki/Sphere_eversion

Many thanks for that but I have to say that I did not understand a word of it. It looks convincing though, so I will accept it.

Dod

Not really surprising because sphere eversion is not an everyday idea. It is part of an esoteric mathematical topic called differential topology which in turn is a branch of topology which itself is part of the dry mathematical concept of set theory. It's more about following through a logical series of rules than real life. So sphere eversion is not about real spheres but rather certain conceptual properties of the spherical shape.

Which is to say you cannot turn an actual real tennis ball inside out!

GS

[Dod101]

Many thanks for that but I have to say that I did not understand a word of it. It looks convincing though, so I will accept it.

Dod

Not really surprising because sphere eversion is not an everyday idea. It is part of an esoteric mathematical topic called differential topology which in turn is a branch of topology which itself is part of the dry mathematical concept of set theory. It's more about following through a logical series of rules than real life. So sphere eversion is not about real spheres but rather certain conceptual properties of the spherical shape.

Which is to say you cannot turn an actual real tennis ball inside out!

GS

Thanks for the explanation. Mathematicians love concepts and theories of course.

Dod

[didds]

Thanks for the explanation. Mathematicians love concepts and theories of course.

Dod

Yup!

probably the most obvious being "i" - the square root of -1. It can't actually exist ... but the concept and its use opens up whole branches of maths that otherwise couldn't exist (or would require some other esoteric invention/concept!)

[stewamax]

In other thread (https://www.lemonfool.co.uk/viewtopic.php?p=579698#p579698) I noted that – mathematical physicists apart – we have to rely on earthly analogies to try to understand how the world actually works. The man in the street is not, perhaps, the best person to ask about the mathematical jiggery-pokery that is the basis of eversion of a theoretical tennis ball. The folding of lavatory paper is at least demonstrable.

Something just as weird: imagine a photon of light starting its journey at the time of the Big Bang nearly 14 billion years ago. Since then, it has been travelling through space without incident until, after all that time, it finally arrives at Earth and we see it. The photon is still as fresh as a daisy because it is as if it had just left the Big Bang: to it, no time has elapsed at all.
(And Roger Penrose's fairly recent proposal that, when the Universe has expanded and cooled to the extent such that all is left is a rarefied collection of photons, this IS the next Big Bang, defies any analogy whatever).

[UncleEbenezer]

Thanks for the explanation. Mathematicians love concepts and theories of course.

Dod

Yup!

probably the most obvious being "i" - the square root of -1. It can't actually exist ... but the concept and its use opens up whole branches of maths that otherwise couldn't exist (or would require some other esoteric invention/concept!)

Um ...

It can actually exist, in a rather similar sense to how -1 can actually exist.

Or arguably to how 1 (the number, not as in one thing) can exist.

(Please just don't produce a number two in this thread).

[TUK020]

... I am not sure I understand about a tennis ball.
Dod

seems this explains (?!) it all...

https://en.wikipedia.org/wiki/Sphere_eversion

not sure how "allowing self-intersections of the sphere's surface" means not cutting or creasing the surface

[XFool]

So sphere eversion is not about real spheres but rather certain conceptual properties of the spherical shape.

Which is to say you cannot turn an actual real tennis ball inside out!

Now you tell me!

[UncleEbenezer]

So sphere eversion is not about real spheres but rather certain conceptual properties of the spherical shape.

Which is to say you cannot turn an actual real tennis ball inside out!

Now you tell me!

It's easy if you allow yourself four (or more) dimensions.

Demo: take an elastic band. Lay it flat with no twists. Now you can easily turn it inside out and barely (if at all) see the difference. You're working in three dimensions with the two-dimensional counterpart to a hollow sphere like a tennis ball.

[servodude]

Now you tell me!

It's easy if you allow yourself four (or more) dimensions.

Demo: take an elastic band. Lay it flat with no twists. Now you can easily turn it inside out and barely (if at all) see the difference. You're working in three dimensions with the two-dimensional counterpart to a hollow sphere like a tennis ball.

So "just give it time"?

[stewamax]

The secret of Djokovic's success in the Garros - secret practice with Uri Geller?

[didds]

seems this explains (?!) it all...

https://en.wikipedia.org/wiki/Sphere_eversion

not sure how "allowing self-intersections of the sphere's surface" means not cutting or creasing the surface

and I'd agree!

[XFool]

seems this explains (?!) it all...

https://en.wikipedia.org/wiki/Sphere_eversion

not sure how "allowing self-intersections of the sphere's surface" means not cutting or creasing the surface

Yes. It seemingly isn't even hard to understand how to do it, if you can do things like that! Just push it inside out through itself...

Though, that might also bring us back on topic.

[Paultry]

When I re-jigged the bathroom and under-the-stairs loo I fitted what are known as loo syphons.

They are basically a hand held shower outlet with a trigger, used to wash ones nether regions. Found extensively in the middle east.

I rigged the first one to a 8KW instant hot water system so that warm water could be readily available. The second one was straight off the side of the loo, so only cold water.

In practice the cold water one turns out not to be as alarming as you might imagine.

Theoretically you no longer require loo paper, but I'm not the only one who lives here.

Paul